


"""simple docstring"""
from math import isqrt, loga

def 				_snake_case      (   __snake_case							:      int   ):




   """simple docstring"""







   _lowerCamelCase	:					List[str]   =		[True] * max_number
   for i in range(2						, isqrt(max_number - 1   ) + 1   ):
      if is_prime[i]:
         for j in range(i**2						, __snake_case						, __snake_case   ):
            _lowerCamelCase	:					Optional[int]   =		False

   return [i for i in range(2						, __snake_case   ) if is_prime[i]]

def 				_snake_case      (   __snake_case							:      int = 800800						, __snake_case							:      int = 800800   ):




   """simple docstring"""







   _lowerCamelCase	:					Union[str, Any]   =		degree * loga(__snake_case   )
   _lowerCamelCase	:					Union[str, Any]   =		int(__snake_case   )
   _lowerCamelCase	:					Dict   =		calculate_prime_numbers(__snake_case   )

   _lowerCamelCase	:					Optional[int]   =		0
   _lowerCamelCase	:					Any   =		0
   _lowerCamelCase	:					Any   =		len(__snake_case   ) - 1
   while left < right:
      while (
          prime_numbers[right] * loga(prime_numbers[left]   )
          + prime_numbers[left] * loga(prime_numbers[right]   )
          > upper_bound
      ):
         right -= 1
      hybrid_integers_count += right - left
      left += 1

   return hybrid_integers_count


if __name__ == "__main__":
 print(f'''{solution() = }''')





import numpy as np
def 							UpperCamelCase_(					_A :np.array	)->		np.array:
			return 1 / (1 + np.exp(-vector	))


if __name__ == "__main__":
						import doctest

						doctest.testmod()


